Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search


FM Harmonic Amplitudes (Bessel Functions)

FM bandwidth expands as the modulation-amplitude $ A_m$ is increased in (G.2) above. The $ k$ th harmonic amplitude is proportional to the $ k$ th-order Bessel function of the first kind $ J_k$ , evaluated at the FM modulation index $ \beta=A_m$ . Figure G.7 illustrates the behavior of $ J_k(\beta)$ : As $ \beta $ is increased, more power appears in the sidebands, at the expense of the fundamental. Thus, increasing the FM index brightens the tone.

Figure: Bessel functions of the first kind for a range of orders (harmonic numbers) $ k$ and argument (FM index) $ \beta $ (from [264]).
\includegraphics[width=\twidth]{eps/bessel}


Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

[How to cite this work]  [Order a printed hardcopy]  [Comment on this page via email]

``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2016-07-18 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA